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geom3d

  

reflection

  

find the reflection of a geometric object in a point, in a line, or in a plane

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

reflection(Q, P, c)

Parameters

Q

-

the name of the object to be created

P

-

geometric object

c

-

point, line, or plane

Description

• 

In reflection in a point, each point P of the set S of all points of unextended space is carried into the point P1 of S such that PP1 is bisected by a fixed point O of space.

• 

In reflection in a line, each point P of S is carried into the point P1 of S such that PP1 is perpendicularly bisected by a fixed line l of space.

• 

In reflection in a plane, each point P of S is carried into the point P1 of S such that PP1 is perpendicularly bisected by a fixed plane p of space.

• 

For a detailed description of the object created Q, use the routine detail (i.e., detail(Q))

• 

The command with(geom3d,reflection) allows the use of the abbreviated form of this command.

Examples

withgeom3d:

Define the plane oxy.

planeoxy,pointC,0,0,0,pointX,1,0,0,pointY,0,1,0:

Define the sphere with center (1,1,1) and radius 2.

spheres,pointo,1,1,1,2

s

(1)

Find the reflection of the sphere s in the plane oxy.

reflections1,s,oxy

s1

(2)

details1

Warning, assume that the name of the axes are _x, _y and _z

name of the objects1form of the objectsphere3dname of the centercenter_s1_1coordinates of the center1,1,−1radius of the sphere2surface area of the sphere16πvolume of the sphere32π3equation of the sphere_x2+_y2+_z22_x2_y+2_z1=0

(3)

Check that s and s2, the reflection of s1, are the same.

reflections2,s1,oxy

s2

(4)

AreDistincts,s2

false

(5)

Plot the sphere, its reflection and the plane.

draws,s1,oxy,style=patch,lightmodel=light4

See Also

geom3d[objects]

geom3d[transformation]

 


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